Question

Choose the polynomial written in standard form. x2 4x4 10x6 x4 4x3 10x x7 4x3 10x4 x6 4x3 10x7

Answer 1

The polynomial that is written in standard form out of the given options is given by: Option 2: x^4 + 4x^3 + 10x

What is standard form of a polynomial?

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which the terms with higher exponents are written on left side to those which have lower exponents.

What are terms in polynomials?

Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.

Example:

$x^3 + 3x +5$

is a polynomial consisting 3 terms as $x^3, 3x \: \rm and \: 5$

Cheking all the options for them being in standard form or not:

• Option 1: $x^2 + 4x^4 + 10x^6$

Second term has 4 as exponent, but on its left, the first term has 2 as exponent. So higher expoent holding term is not on left. Thus, this polynomial is not in standard form.

• Option 2: $x^4 + 4x^3 + 10x$

4 > 3 > 1 (comparing the exponents), and the terms holding them are also in this order (left to right).

Thus, this polynomial is in standard form.

• Option 3: $x^7 + 4x^3 + 10x^4$

Not in standard form because the last term has bigger power then the term on its left.

• Option 4: $x^6 + 4x^3 + 10x^7$

Not in standard form because the last term has bigger power then the term on its left.

Thus, the polynomial that is written in standard form out of the given options is given by: Option 2: x^4 + 4x^3 + 10x

Learn more about standard form of a polynomial here:

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